Finite Group Databasebeta

← #25132747

Subgroups — #25132747

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D43C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3C4×#13063301C211yesmaximal, characteristic
4#19135935C211yesmaximal, characteristic, complemented
5#19135931C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135744C211yesmaximal, characteristic, complemented
8#19135553C211yesmaximal, characteristic, complemented
9#19135550C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic
11#19134899C211yesmaximal, characteristic
12#19134786C211yesmaximal, characteristic
13#19134781C211yesmaximal, characteristic
14#19134572C211yesmaximal, characteristic
15C2×C43×#479C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C2×#13063315—21no—
20C2×#13063315—21no—
21#125×D43—24no—
22#125×D43—24no—
23C2×#13063301C2211yescharacteristic
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43—21no—
26C2×C4⋊C4×D43C2211yescharacteristic
27C2×C4⋊C4×D43C2211yescharacteristic
28C2×C42×D43C2211yescharacteristic
29#14583206—24no—
30C2×#13063258C2211yescharacteristic
31C2×#13063256C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582780—21no—
40#14582770—21no—
41#14582756C2211yescharacteristic
42C4×Dic43⋊C4—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#479—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43D411yescharacteristic
66C22×C4×D43D411yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063317—22no—
71#13063317D414yes—
72#13063316—22no—
73#13063316—22no—
74#13063316—22no—
75#13063316—22no—
76#13063315—28no—
77#13063315—28no—
78#13063301—22no—
79#13063301Q814yes—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C4⋊C4×D43—28no—
95C4⋊C4×D43—28no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43—22no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106C42×D43—22no—
107C42×D43—22no—
108#13063258—22no—
109#13063256—22no—
110C4⋊(C43⋊C8)—22no—
111#13063249—22no—
112#13063249—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×Q8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123#125×C43—22no—
124#125×C43D414yes—
125C4×Q8×C43—22no—
126C4×Q8×C43—22no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—22no—
136#106×C43—22no—
137C4⋊C8×C43—22no—
138#103×C43—22no—
139#103×C43—22no—
140C23×D43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×Q812yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—24no—
166C2×C4×D43—24no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—41no—
172C2×C4×D43—41no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43C2×Q812yes—
178C2×C4×D43#4112yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C4⋊C4×C43—24no—
186C4⋊C4×C43—24no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43C2×D412yes—
193C4⋊C4×C43C2×D412yes—
194C42×C43—42no—
195C42×C43C2×D412yes—
196C42×C43C2×D412yes—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—42no—
199C4⋊Dic43—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C2×D412yes—
207C4⋊Dic43C2×D412yes—
208C4⋊Dic43C2×Q812yes—
209Dic43⋊C4—24no—
210Dic43⋊C4—24no—
211Dic43⋊C4—24no—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—42no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—42no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C23×C43C22×D411yescharacteristic
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43C22⋊Q812yes—
234C22×D43#13512yes—
235C22×D43#13712yes—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—41no—
239Q8×C43—41no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43#12012yes—
257C2×C4×C43#12012yes—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×Q811yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43C22⋊Q812yes—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—44no—
290C4×D43—44no—
291C4×D43—48no—
292C4×D43—48no—
293C8×C43—41no—
294C8×C43—41no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297#24307—431nomaximal, Sylow
298C22×C43C2×#12011yescharacteristic
299C22×C43C2×C22⋊Q811yescharacteristic
300C22×C43#53611yescharacteristic
301C22×C43C2×#13511yescharacteristic
302C22×C43C2×#13711yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57511yescharacteristic
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—22no—
311C2×D43#47914yescomplemented
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—42no—
316C4×C43—42no—
317C4×C43—81no—
318C4×C43#54811yescharacteristic
319C4×C43#54811yescharacteristic
320C4×C43D4×Q811yescharacteristic
321C4×C43D4×Q811yescharacteristic
322Dic43—22no—
323Dic43—42no—
324Dic43—41no—
325Dic43—42no—
326Dic43—41no—
327Dic43—42no—
328Dic43—81no—
329C22×#125—431no—
330C2×#479—431no—
331C2×#479D4311yescharacteristic, complemented
332C4×C22⋊Q8—431no—
333#2059—431no—
334#2059—431no—
335#2026—431no—
336#2026—431no—
337#1989—431no—
338#1989—431no—
339#1872—431no—
340#1872—431no—
341#1853—431no—
342#1852—431no—
343#1797—431no—
344C2×C43#240911yescharacteristic
345C2×C43#300211yescharacteristic
346C2×C43#300711yescharacteristic
347C2×C43C2×#47911yescharacteristic
348C2×C43#308011yescharacteristic
349C2×C43#323211yescharacteristic
350C2×C43#323611yescharacteristic
351D43—24no—
352C2×#125—431no—
353C2×#125—431no—
354C2×#125—431no—
355C2×#125—861no—
356C2×#125—861no—
357C2×#125—864no—
358C2×#125—864no—
359C2×#125C2×D4311yescharacteristic
360C2×C22⋊Q8—431no—
361C2×C4×Q8C2×D4311yescharacteristic
362C22×C4⋊C4—431no—
363C22×C4⋊C4—431no—
364C22×C4⋊C4—861no—
365C22×C4⋊C4—861no—
366C22×C42—431no—
367#479—24no—
368#479—864no—
369C2×#107—431no—
370C2×#107C2×D4311yescharacteristic
371C2×#106—431no—
372C2×#106C2×D4311yescharacteristic
373C2×C4⋊C8—431no—
374C2×C4⋊C8C2×D4311yescharacteristic
375C2×#103—431no—
376C2×#103—431no—
377C2×#103C2×D4311yescharacteristic
378C2×#103C2×D4311yescharacteristic
379C2×C22⋊C8—431no—
380C2×C22⋊C8—431no—
381#391—431no—
382#389—431no—
383#387—861no—
384#385—861no—
385#380—431no—
386C4×C4⋊C4—431no—
387C4×C4⋊C4—861no—
388C4×C22⋊C4—861no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397#336—431no—
398#336—431no—
399C43#2430711yescharacteristic, complemented, Sylow
400C22×Q8C22×D4311yescharacteristic
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—431no—
404C23×C4—861no—
405C23×C4—861no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#125—22no—
411#125—434no—
412#125—862no—
413#125—862no—
414#125—868no—
415#125—868no—
416#125—862no—
417#125—862no—
418#125—862no—
419#125C22⋊D4314yes—
420C22⋊Q8—434no—
421C22⋊Q8—862no—
422C4×Q8—22no—
423C4×Q8—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—862no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—868no—
434C2×C4⋊C4—868no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C42—21no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—862no—
457C2×C42—862no—
458C2×C42—861no—
459C2×C42C22×D4311yescharacteristic
460#107—22no—
461#107—862no—
462#106—22no—
463#106—862no—
464C4⋊C8—22no—
465C4⋊C8—862no—
466#103—22no—
467#103—22no—
468#103—862no—
469#103—862no—
470C22⋊C8—862no—
471C22⋊C8—862no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477C24—431no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8Q8×D4312yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—431no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—864no—
496C22×C4—864no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—861no—
507C22×C4—1721no—
508C22×C4—1721no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4—1722no—
513C22×C4D4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—432no—
536C4⋊C4—432no—
537C4⋊C4—432no—
538C4⋊C4—864no—
539C4⋊C4—864no—
540C4⋊C4—864no—
541C4⋊C4—864no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—864no—
545C4⋊C4—864no—
546C4⋊C4—864no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—1722no—
553C4⋊C4C2×C22⋊D4312yes—
554C4⋊C4C2×C22⋊D4312yes—
555C22⋊C4—864no—
556C22⋊C4—1722no—
557C42—42no—
558C42—862no—
559C42—862no—
560C42—861no—
561C42—861no—
562C42—1722no—
563C42D4×D4312yes—
564C42C2×C22⋊D4312yes—
565C23—432no—
566C23—432no—
567C23—432no—
568C23—861no—
569C23—861no—
570C23—861no—
571C23—861no—
572C23C2×D4×D4311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—432no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—1724no—
610C2×C4—1724no—
611C2×C4—1728no—
612C2×C4—1728no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4#1306329312yes—
623C2×C4#1306329312yes—
624C2×C4C2×D4×D4311yescharacteristic
625C2×C4C22×C22⋊D4311yescharacteristic
626C2×C4C2×Q8×D4311yescharacteristic
627C2×C4#41×D4311yescharacteristic
628C2×C4#1306337211yescharacteristic
629C2×C4#1306337311yescharacteristic
630C8—41no—
631C8—41no—
632C8—1721no—
633C8—1721no—
634C22—434no—
635C22—862no—
636C22—862no—
637C22—862no—
638C22—862no—
639C22—862no—
640C22—862no—
641C22C2×#1306329311yescharacteristic
642C22C22⋊Q8×D4311yescharacteristic
643C22#1458347211yescharacteristic
644C22#135×D4311yescharacteristic
645C22#137×D4311yescharacteristic
646C22#1458369611yescharacteristic
647C22#1458369811yescharacteristic
648C4—22no—
649C4—22no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—862no—
655C4—3441no—
656C4—1721no—
657C4—1722no—
658C4—1721no—
659C4—1722no—
660C4—1722no—
661C4#1458355611yescharacteristic
662C4#1458355911yescharacteristic
663C4#1458356211yescharacteristic
664C4Q8×C22⋊D4311yescharacteristic
665C2—864no—
666C2#1913795611yescharacteristic
667C2#1914380911yescharacteristic
668C2#1914385111yescharacteristic
669C2#479×D4311yescharacteristic
670C2#1914441411yescharacteristic
671C2#1914576711yescharacteristic
672C2#1914579911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#479D43
hypocenterC43#24307
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
4. #19135935C2semidirect
5. #19135931C2semidirect
6. #19135744C2semidirect
7. #19135744C2semidirect
8. #19135553C2semidirect
9. #19135550C2semidirect
15. C2×C43×#479C2semidirect
311. C2×D43#479semidirect
331. C2×#479D43semidirect
399. C43#24307semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#125×D432
C2×#145832062
C4×#130633012
#191359352
#191359312
#191357442
#191355532
#191355502
#191348992
#191347862
#191347812
#191345722
C2×C43×#4792
#2430743